What is the value of the two-digit number TU, where T represents the tens digit and U represents the units digit?(1) T × U² = 196(2) 3T + 5U = 47

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.C. Statements (1) and (2) TAKEN TOGETHER are sufficientto answer the question, even though NEITHER statement BY ITSELF is sufficient.D. Either statement BY ITSELF is sufficient to answer thequestion.E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient toanswer the question, meaning that further information would be needed to answer the question.

(A) Since T and U are digits in a number, they must both be integers between 0 and 9 inclusive. In fact, T must be between 1 and 9 inclusive, since it is the tens digit.

Statement (1) tells us that (T) × (U²) = 196. From here, we should take the prime factorization of 196 to help us solve for T and U:196 factors into 2 × 2 × 7 × 7.

Since we need to collect the prime factors in such a way that we get a digit times the square of another digit, U² must be 7²and T must be 4. If U² were 2², then T would be 49, which is impossible if T is to be a digit. So T = 4, U = 7, and the number TU = 47. Statement (1) is sufficient.

Using Statement (2), we need to substitute possible values forT and determine which one(s) yield possible values for U (remember, U must be a positive integer less than 10). If T = 4, then U = 7, and if T = 9, then U = 4. Therefore, TU could be 47 or 94. Statement (2) is not sufficient.

Since Statement (1) is sufficient and Statement (2) is not, thecorrect answer is choice (A).-------------

It's not mentioned if TU is +ve integer or a -ve integer. Now consider U = -7, then U² becomes +ve and TU²2 is still 196. So for statement 1 we can have two solns -47 or +47.

Are you saying that, once we validate that statement I is sufficient, if the values don't match statement II, we can consider II insufficient?

NO. We found the definite value using the statement (1) and it will satisfy the statement (2) as well. But if we use the statement (2) by itself there will also be other possible values of TU. Thus we will NOT be able to know the definite value of TU based on the statement (2) alone.

In other words, we can conclude that the statement (2) is insufficient if we show that two different outcomes, based on the statement (2), are possible. By two different outcomes we understand those that answer the main question differently.

In case of this problem we have:

Quote:

If T = 4, then U = 7, and if T = 9, then U = 4. Therefore, TU could be 47 or 94. Statement (2) is not sufficient.

As you can see the two possible numbers, 47 and 94, both satisfy statement (2) but are different values of the number TU. So the question cannot be answered definitely using the statement (2) alone.

Why do you need the prime factors and is there a smart way to get to all the prime factors quickly?

We need the prime factorization of 196 to see what the digits T and U can be. Especially U, because we have T × U² = 196 and thus U² must be a product of pairs, for example (2 × 2), or (7 × 7), or (2 × 2) × (7 × 7). In this case the latter does not fit, because U is a digit.

How to get prime factors of N quickly? 1. Start with dividing by 2, 5, or (2 × 5) = 10.These are easy to spot. If the number is even, then divide it by 2 until it becomes odd.If the number ends in 5 or 0, then it is divisible by 5.N = (2 × … × 2)(5 × … × 5) × M

2. Then check if 3 is a factor.If the sum of the digits of a number is divisible by 3, then the number itself is divisible by 3.N = (2 × … × 2)(5 × … × 5) × (3 × … × 3) × K

3. Now you have the remaining number, K. All you are left to do is to check other primes from 7 and up till √KWhy do we check below √K only? Because if there is a prime divider greater than √K, let's say x, then there will be a divider K/x (below √K).

But the third step won't be hard in gmat. The number K will be either a square of a prime number, or divisible by 7 or 11, for example 77.

Who is online

Users browsing this forum: No registered users and 1 guest

You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forumYou cannot post attachments in this forum

GMAT(TM) and GMAT CAT (TM) are registered trademarks of the Graduate Management Admission Council(TM). The Graduate Management Admission Council(TM) does not endorse, nor is affiliated in any way with the owner or any content of this site.